*Gas Laws*Purpose of the Experiment

To demonstrate the complexities involved in measuring properties of gases related to:

1.) Complications in weighing due to the buoyancy of air;

2.) Problems in pressure measurements over water; and,

3.) Non-ideality of Gases.

Physical Characteristics of GasesPhysical Characteristics Typical Units

Volume, V liters (L)

Pressure, P atmosphere(1 atm = 1.015x105 N/m2)

Temperature, T Kelvin (K)

Number of atoms or molecules, n

mole (1 mol = 6.022x1023 atoms or molecules)

Pressure and volume are inversely related at constant temperature.

PV = K

As one goes up, the other goes down.

P1V1 = P2V2

Boyle’s Law

“Father of Modern Chemistry”Robert Boyle

Chemist & Natural PhilosopherListmore, Ireland

January 25, 1627 – December 30, 1690

Boyle’s Law: P1V1 = P2V2

Boyle’s Law: P1V1 = P2V2

Volume of a gas varies directly with the absolute temperature at constant pressure.

V = KT

V1 / T1 = V2 / T2

Charles’ Law

Jacques-Alexandre CharlesMathematician, Physicist, Inventor

Beaugency, FranceNovember 12, 1746 – April 7, 1823

Charles’ Law: V1/T1 = V2/T2

Charles’ Law: V1/T1 = V2/T2

At constant temperature and pressure, the volume of a gas is directly related to the number of moles.

V = K n

V1 / n1 = V2 / n2

Avogadro’s Law

Amedeo AvogadroPhysicist

Turin, ItalyAugust 9, 1776 – July 9, 1856

Avogadro’s Law: V1/n1=V2/n2

At constant volume, pressure and absolute temperature are directly related.

P = k T

P1 / T1 = P2 / T2

Gay-Lussac Law

Joseph-Louis Gay-LussacExperimentalistLimoges, France

December 6, 1778 – May 9, 1850

The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container.

The total pressure is the sum of the partial pressures.

PTotal = P1 + P2 + P3 + P4 + P5 ...

(For each P = nRT/V)

Dalton’s Law

John DaltonChemist & Physicist

Eaglesfield, Cumberland, EnglandSeptember 6, 1766 – July 27, 1844

Dalton’s Law

Water evaporates!

When that water evaporates, the vapor has a pressure.

Gases are often collected over water so the vapor pressure of water must be subtracted from the total pressure.

Vapor Pressure

Differences Between Ideal and Real Gases

Obey PV=nRT Always Only at very low P and high T

Molecular volume Zero Small but nonzero

Molecular attractions Zero Small

Molecular repulsions Zero Small

Ideal Gas Real Gas

Real molecules do take up space and do interact with each other (especially polar molecules).

Need to add correction factors to the ideal gas law to account for these.

Real Gases

Ideally, the VOLUME of the molecules was neglected:

 

at 1 Atmosphere Pressure

at 10 Atmospheres Pressure

at 30 Atmospheres Pressure

Ar gas, ~to scale, in a box 3nm x 3nm x3nm

The actual volume free to move in is less because of particle size.

More molecules will have more effect.

Corrected volume V’ = V – nb

“b” is a constant that differs for each gas.

Volume Correction

But since real gases do have volume, we need:

Because the molecules are attracted to each other, the pressure on the container will be less than ideal.

Pressure depends on the number of molecules per liter.

Since two molecules interact, the effect must be squared.

Pressure Correction

2observed )

V

n( aPP

[Pobs a (n

V)2] (V nb) nRT

Corrected Pressure Corrected Volume

Van der Waal’s equation

“a” and “b” are determined by experiment “a” and “b” are different for

each gas bigger molecules have larger

“b” “a” depends on both size and

polarity

Johannes Diderik van der WaalsMathematician & Physicist

Leyden, The NetherlandsNovember 23, 1837 – March 8, 1923

Compressibility Factor

The most useful way of

displaying this new law

for real molecules is to

plot the compressibility

factor, Z :

For n = 1

Z = PV / RT 

Ideal Gases have Z = 1

Part 1: Molar Volume of Butane

Page 72-73in your

Green Book

Molar mass of butane (C4H10) = __________ g/mole

Mass of butane: __________

n or nB= _______

Molar mass of butane (C4H10) = __________ g/mole

(12.011 4) + (1.008 10) = 58.124

Mass of butane: __________

Initial weight of cartridge – final weight of cartridge

n or nB= _______

butane of massMolar

butane of mass

T = ____ K P = _____atm 0.500 L

Ask your TA for theLab temperature and Pressure*

Note: K = oC + 273.15 & 1 atm = 760 torr

Apparent molar volume, (Vm = V / n) of butane

at experimental T & P: Vm = ________ L / mole

V/n n → Calculated earlier0.500 L

*These will be posted on the chalkboard. Verify the values are for your session before posting in your book.

T = ____ oC P = _____torr V = _____L

Apparent molar volume of butane at STP; Vm = _____L/mole

2

22

1

11

T

V P

T

V P

Lab pressure

Lab temperature(K)

0.500 L1 atm or 760 torr

273.15 K

calculate

n

VVm

Already calculated

V2calculate

Partial pressure of water vapor in flask: Pw = ______torr

2

2

vdw V

n a

b)n (V

T Rn P

T

5300 20.943Pw T

5300 20.943)(lnP x w torr

Lab temperature(K)

calculate

xetorr )(Pw

Partial pressure of butane in flask: _________ torr _________atm

PB = Ptotal -Pw

Lab pressure(torr)

calculated in previous step

(torr)

calculate

2

2

vdw V

n a

b)n (V

T Rn P

Partial pressure of butane: Pvdw = ________ atm

0.08206 L.atm/mole. K

Lab temp.Already calculated

0.500 L0.1226 L/mole

0.500 L

14.47 atm .L2/mole2

calculate

Compressibility factor for butane : ZB = ________

T R n

V P Z

B

BB

T R n

V P Z

B

BB

Partial pressure of butane in flask (atm)Calculated earlier

0.500 L

Lab temperature(K)

0.08206 L.atm/mole. Ksame as “n”

already calculated

calculate

Estimated second Virial Coefficient for Butane at room temperature:

BB = ___________L/mole

n

V ) 1 (ZBB

n

V ) 1(ZB BB

Calculated in previous stepCompressibility factor for butane

0.500 L

already calculatedcalculate

Part 2: Buoyancy EffectFilling Ziplok bag with butane gas

Page 75in your

Green Book

Discrepancy is the difference between these two masses

Initial mass cartridge________g bag _________ gFinal mass ________g __________gChange in mass ________g __________g

Discrepancy: _________g

Moles of Butane in bag: n = _____ moles

massMolar

massn

Change in cartridge mass

58.124 g/mole

calculate

Calculated volume of Butane in bag: ____L

1)(Z

Bn V

1)(Z

Bn V

B

B

Calculated in previous step

Estimated second Virial Coefficient for Butane at room temperature

Calculated in Part 1 (p 73).

Compressibility factor for ButaneCalculated in Part 1 (p 73).

calculate

Estimated density of air at experimental T and P: d= ____g / L

volume

massd volume

massd

Calculated volume of Butane in bag(calculated in previous step)

Buoyancy effect of displaced volume of air(the mass discrepancy)

calculate

Estimated Molar mass of air: _____g/mole

P

T R dM P

T R dM

Lab pressure(atm)

Lab temperature

(K)

0.08206 L.atm/mole. KEstimated density of air(calculated in previous step)

calculate

Part 3: Conservation of MassGas generating reaction in a closed system

Page 77in your

Green Book

Molar mass of NaHCO3 : _____g/mole

Moles of NaHCO3: _______ mole

Part 3: Conservation of MassGas generating reaction in a closed system

Molar mass of NaHCO3 : _____g/mole

(22.990) + (1.008) + (12.011) + (3 15.999) = 84.006 g/mole

Moles of NaHCO3: _______ mole

massMolar

massmoles

Part 3: Conservation of MassGas generating reaction in a closed system

Weight of bag and reaction components:Before reaction: _____ g after reaction : ______ g

Discrepancy: _____g

Discrepancy is the difference between these two weights.

Estimated volume of expansion: _______ L

air ofdensity

ydiscrepancweight V

Determined in Part 2 (p 75).

calculate

Reaction:1 NaHCO3(aq) + CH3CO2H(aq) _____ + 1 CO2(g) + ______

Expected moles of CO2(gas) : ___________ moles

Expected volume of gas at laboratory T & P: _____L

atm

W

atm

CO

gas

PP1

PRTn

V

2

Lab temp. (K)0.08206 L.atm/mole.K

Lab pressure (atm)

Partial pressure of water vapor. (Note: Convert your Pw to atm.) (You calculated Pw in torr in Part 1 – p 73.)

calculateLab pressure (atm)

Expected moles of CO2 (from previous step)

1000 ml beaker 500 ml volumetric flask Tygon tubing with Hook Butane cylinder 1 piece of plastic wrap 1 quart Ziploc Bag 5 dram vial with lid*

In The Hood: 50% Acetic Acid in a

500 ml plastic dispenserBy Balances: Sodium bicarbonate, NaHCO3

Check Out from the Stockroom

Clean Up:*Dispose of liquid waste in appropriate container. Rinse vial and lid with water

and return them to the stockroom.

Hazards:50% Acetic acid (corrosive, sharp, irritating odor)Butane (flammable)

Waste:5 gallon liquid waste for NaHCO3 and acetic acid

Read: Thermochemistry (Heat of Neutralization & Heat of Fusion)

pp 1-17 – Chapter 1 in the Green Book

Turn In: Gas Laws Experiment pp. 73-77 + calculations page.

For Next Week – March 5-8

Calculations must be shown on a separate piece of paper, with units to the correct number of significant figures. Datasheets need to be in ink, but calculations may be done with pen or pencil.

Calculations scribbled in the margins of the lab pages are NOT ACCEPTABLE.